Inventiones mathematicae

, Volume 93, Issue 1, pp 35–76

Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) groups


  • S. L. Woronowicz
    • Instituut voor Theoretische FysicaUniversität Leuven

DOI: 10.1007/BF01393687

Cite this article as:
Woronowicz, S.L. Invent Math (1988) 93: 35. doi:10.1007/BF01393687


The notion of concrete monoidalW*-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twistedSU(N) groups denoted bySμU(N). It is shown that the representation theory forSμU(N) is similar to that ofSU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.

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© Springer-Verlag 1988